You can increase min wage all you want, if there aren't enough homes in an area for everyone who works full time in that area to have one, you will still have folks who work full time who don't have one. In fact, increasing min wage too much will exacerbate the problem by making it more expensive to build more (and maintain those that exist). Though at some point, it will fix the problem too, because everyone will move and then there will be plenty of homes for anyone who wants one.

I agree with you 100%! Any additional surplus will be extracted as rents, when housing is restricted. I am for passing laws that make it much easier for people to obtain permits to build housing where there is demand. Too much of residential zoning is single-family housing. Texas does a better job at not restricting housing than California, for example. Many towns vote blue, talk to talk, but do not walk the walk.